Re: minor typos in Test doc

On Wed, 13 Aug 2003, Jos De_Roo wrote:

>
>
> That's indeed a nicier style and good for your toner
> (lots of reprints, though with less color this time ;-)
>
> Jeremy, Sean - maybe it's too hot here, but I can't see why
> http://www.w3.org/2002/03owlt/description-logic/inconsistent107.rdf
> is inconsistent (I think I understand why 108 is, but not 107).

It is now less hot here, so I'll have a crack at explaining it! 107
looks like:

[Namespaces:
  owl	= http://www.w3.org/2002/07/owl#
  rdfs	= http://www.w3.org/2000/01/rdf-schema#
  xsd	= http://www.w3.org/2001/XMLSchema#
  rdf	= http://www.w3.org/1999/02/22-rdf-syntax-ns#
  a	= http://oiled.man.example.net/test#
]

Ontology(

 Class(a:Unsatisfiable complete
  intersectionOf(restriction(a:r someValuesFrom a:d)
	         complementOf(restriction(a:r minCardinality(2)))
		 restriction(a:r someValuesFrom a:c)
		 restriction(a:r minCardinality(1))))

 Class(a:a complete
  unionOf(a:c a:d))
 Class(a:c)
 Class(a:d)
 Class(a:e)

 ObjectProperty(a:r)
 ObjectProperty(a:r1)
 ObjectProperty(a:r2)
 ObjectProperty(a:r3)
 ObjectProperty(a:t1)
 ObjectProperty(a:t2)
 ObjectProperty(a:t3)
 ObjectProperty(a:tt)

 Individual(_
  type(a:Unsatisfiable))

 DisjointClasses(a:d a:e)
 DisjointClasses(a:c a:e)
 DisjointClasses(a:c a:d)

 SubPropertyOf(a:t1 a:tt)
 SubPropertyOf(a:t2 a:tt)
 SubPropertyOf(a:t3 a:tt)
 SubPropertyOf(a:r2 a:r)
 SubPropertyOf(a:r1 a:r)
 SubPropertyOf(a:r3 a:r)

)

The role hierarchy is a bit of a red herring here, as is the definition
of a.

The definition of Unsatisfiable says that anything that's an instance of
Unsatisfiable has to have at least 1 r, has to be related to a c via r and
has to be related to a d via r. It must also be related to no more than
one thing via r (the complement of [minCard 2 r] is [maxCard 1 r]). But
this leads to a contradiction as c and d are disjoint.

Does that help?

	Sean

-- 
Sean Bechhofer
seanb@cs.man.ac.uk
http://www.cs.man.ac.uk/~seanb

Received on Wednesday, 13 August 2003 04:55:54 UTC